Both the strong mode confinement and the low propagation loss are longed for designing highly integrated terahertz (THz) devices, but they are difficult to be achieved at the same time. Here, a graphene-coated nanowire with a dropshaped cross section (GNDCS) is proposed with the long-range propagation and strong confinement. We found this waveguide can support two kinds of graphene surface plasmon polaritons (GSPPs), outside-dominant and insidedominant modes, with distinctly different energy distributions. Interestingly, both modes can achieve low-loss propagation with strong mode confinement. In particular, the outside-dominant mode can attain an extremely long propagation length (1mm) and the inside-dominant mode has a very high energy utilization rate. These excellent characteristics make the waveguide very useful in the nanophotonics, bio-photonics and highly integrated THz circuits.